Answer:
The measures of the two angles are 34° and 56°
Step-by-step explanation:
* Lets explain how to solve the problem
- The complementary angles are the angles whose the sum
of their measures is 90°
- The measure of one angle is six more than half the measure
of another angle
- Let the measure of the second angle angle is x
∵ The measure of the 2nd angle is x
∵ The measure of the first angle is 6 more than the half of the
measure of the second angle
∴ The 1st angle is 6 + 1/2 x
∵ The two angles are complementary
∴ The sum of their measures is 90°
∴ x + (6 + 1/2 x) = 90
∴ (x + 1/2 x) + 6 = 90
∴ 3/2 x + 6 = 90
- Subtract 6 from both sides
∴ 3/2 x = 84
- Multiply both sides by
∴ 3x = 168
- Divide both sides by 3
∴ x = 56
∵ x is the measure of the 2nd angle
∴ The measure of the 2nd angle is 56°
∵ The measure of the 1st angle = 6 + 1/2 x
∵ x = 56
∴ The measure of the 1st angle = 6 + 1/2(56) = 34°
* The measures of the two angles are 34° and 56°
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